After selecting a house, you'll be asked to visit Tom Nook's shop as a part-time employee. This is mandatory for paying off your debt, and it serves as the game's tutorial. Use the map Rover gave you in your inventory to find the shop. Its symbol is a yellow leaf. Go to the shop and enter the door to start up a conversation with Tom Nook.
He will give you a work uniform. Bring up your inventory, and put on the work uniform. Talk to Nook to get your first task.
Task 1: Plant flowers and trees around the shop[edit]
You will be given several flowers and saplings to plant around Nook's Shop. To plant something, stand on an empty space of land, open your inventory, and select a packet of flowers or a sapling. You don't need to plant them around Nook's shop; anywhere in the town will do. Once finished, go back to the shop and talk to Nook for Task two.
Task 2: Meet Villagers and Mayor[edit]
Your second task is to introduce yourself to all of your neighbors. If you are in a newly-created town, there will be five of them. You can find where they live on the map; look for the small blue house symbols. The bigger houses on the map are for human residents, so you don't need to check those. Animals will usually be wandering outside there house, but they may also be inside. Go up to a door and press 
to see if an animal is inside or not. You do not need to talk to any animals inside landmarks (such as the town gate or the museum).
You also need to talk to Tortimer, the town mayor, who can be found at the Town Hall. If you think you've met everyone, go back to the shop and talk to Nook. He'll give you your next job if you have it.
Task 3: Deliver furniture[edit]
You will receive a piece of furniture to be delivered to a random villager in town. If you forget, talk to Nook again or check the item in your inventory. Find and talk to the animal, then say "Delivery!" Select the furniture to give it to him or her, and you'll receive a piece of furniture in return. Return to Nook's shop for Task four.
Task 4: Send a letter[edit]
Nook will give you a piece of stationary to write to a specific villager. To write the letter, open your inventory, select the stationary, and select, "Write A Letter." According to Nook, the letter should be a sales pitch, but you can write whatever you want. Once you're finished, go to the town hall and tell the pelican to send the letter to the villager. Go back to Nook's shop and he'll give you Task five. If you lose the stationary along the way, return to Nook and he will give you another one.
Task 5: Deliver carpet[edit]
Nook will give you some carpeting to deliver to a villager. Once it's successfully delivered, you will receive a new carpet for your house. Go back to Nook's shop for task six.
Task 6: Deliver watering can[edit]
Nook will ask you to give a watering can to the same villager you sent a letter to for your fourth task. Complete the delivery, and return to Nook for task seven.
Task 7: Post on the bulletin board[edit]
For your final task, you will be asked to go to the bulletin board by the town hall and post an advertisement for Nook's shop. It doesn't matter what you write. Once you're done, go back to Nook's.
After the seventh task, a small part of your first debt will have been paid off, and you'll be free to do whatever you want. You can return to Nook's shop to buy or sell items, and you can pay off the rest of your debt at the town hall through the bank.